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<p>In this paper, we propose a novel scaling Wigner distribution by integrating the advantages of fractional instantaneous auto-correlation with the linear canonical transform (LCT) framework. We begin by exploring its fundamental properties, including nonlinearity, marginal distributions, time and frequency shifting, conjugate symmetry, convolution behavior, and the anti-derivative relation. A detailed analysis of Moyal’s formula is also presented. To evaluate its performance, the proposed distribution is applied to analyze both the single and bi component linear frequency modulated (LFM) signals. Simulation results clearly demonstrate that the proposed distribution outperforms the conventional Wigner distribution. This improvement is attributed to the increased degrees of freedom offered by the LCT, which enable enhanced time-frequency resolution. Finally, we present an LCSWD-based machine learning approach using CNNs for improved EEG-based seizure detection.</p>

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Novel scaling Wigner distribution in the linear canonical domain

  • 期刊论文

  • 发表日期：

    2025年11月12日

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  • Waseem Z. Lone,
  • Mukul Chauhan,
  • Aamir H. Dar,
  • Amit K. Verma

摘要

In this paper, we propose a novel scaling Wigner distribution by integrating the advantages of fractional instantaneous auto-correlation with the linear canonical transform (LCT) framework. We begin by exploring its fundamental properties, including nonlinearity, marginal distributions, time and frequency shifting, conjugate symmetry, convolution behavior, and the anti-derivative relation. A detailed analysis of Moyal’s formula is also presented. To evaluate its performance, the proposed distribution is applied to analyze both the single and bi component linear frequency modulated (LFM) signals. Simulation results clearly demonstrate that the proposed distribution outperforms the conventional Wigner distribution. This improvement is attributed to the increased degrees of freedom offered by the LCT, which enable enhanced time-frequency resolution. Finally, we present an LCSWD-based machine learning approach using CNNs for improved EEG-based seizure detection.